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Lecture 6

Lecture 6. CSE 331 Sep 10, 2012. Homeworks. HW 1 posted online: see blog/piazza. Pickup graded HW 0 in TA OHs. Suggestions for Piazza. Email them: team “ at ” piazza “ dot ” com. Lecture pace. Mid-term. Online Office Hours. Tomorrow: 9:30pm to 10:30pm. Stable Marriage problem.

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Lecture 6

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  1. Lecture 6 CSE 331 Sep 10, 2012

  2. Homeworks HW 1 posted online: see blog/piazza Pickup graded HW 0 in TA OHs

  3. Suggestions for Piazza Email them: team “at” piazza “dot” com

  4. Lecture pace Mid-term

  5. Online Office Hours Tomorrow: 9:30pm to 10:30pm

  6. Stable Marriage problem Input:M and W with preferences Output: Stable Matching Set of men M and women W Preferences (ranking of potential spouses) Matching (no polygamy in M X W) Perfect Matching (everyone gets married) m w Instablity m’ w’ Stable matching = perfect matching+ no instablity

  7. Two Questions Does a stable marriage always exist? If one exists, how quickly can we compute one? Answer both Qs in +ve by the Gale-Shapley algorithm

  8. Gale-Shapley Algorithm (er, not Nobel prize winners, at least not yet) Women do all the proposing (different from the book) Everyone is in one of three states: free, engaged and married Step 1: A free woman w proposes to her most preferred man m. (m,w) get engaged General step: A free woman w proposes to her top unproposed man m.

  9. Questions/Comments?

  10. Gale-Shapley Algorithm Intially all men and women are free While there exists a free woman who can propose Let w be such a woman and m be the best man she has not proposed to w proposes to m If m is free (m,w) get engaged Else (m,w’) are engaged If m prefers w’ to w w remains free Else (m,w) get engaged and w’ is free Output the engaged pairs as the final output

  11. Preferences Mal Inara Wash Zoe Simon Kaylee

  12. GS algorithm: Firefly Edition Inara Mal Zoe Wash 4 5 6 1 2 3 Kaylee Simon 4 5 6 1 2 3

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